Multipolar interactions in f -electron systems: The paradigm of actinide dioxides

A review is given of the physical properties, composition and crystal structure of intermetallic compounds formed between rare-earth elements and non-magnetic metals, with emphasis on the magnetic properties. Included are the properties of compounds in which the non-rare-earth component is a 4d or 5d transition element. Special consideration is given to the properties of pseudo-binary compounds. Results of magnetisation measurements, neutron diffraction and neutron scattering are discussed together with results derived from NMR, ESR and Mossbauer effect spectroscopy. An evaluation is given of the relevance of the experimental results with respect to different types of exchange interactions in this class of intermetallics. Special consideration is also given to the influence of crystal field effects on the magnetic properties and, furthermore, to the occurrence of intermediate valences in several of the compounds of Ce, Sm, Eu and Yb.

https://iopscience.iop.org/article/10.1088/0034-4885/42/8/003/pdf

Intermetallic compounds of rare earths and non-magnetic metals

Analysis of available experimental data shows that there exists a limited variety of shapes of temperature dependence of spontaneous magnetization. For most metallic ferromagnets the shape (as opposed to scale) of the ${M}_{s}$ versus $T$ curve can be characterized by a single dimensionless parameter. A numerical description of the dependence ${M}_{s}(T)$ for a particular ferromagnetic material is thus reduced to evaluating three quantities: the saturation magnetization ${M}_{0}\ensuremath{\equiv}{M}_{s}(0)$, the Curie point ${T}_{C}$, and the shape parameter $s$. It is demonstrated that classical spin ($S=\ensuremath{\infty}$) dynamics fails to describe correctly either of the finite-temperature characteristics, ${T}_{C}$ or $s$.

Shape of temperature dependence of spontaneous magnetization of ferromagnets: quantitative analysis.

https://iopscience.iop.org/article/10.1088/1674-1056/25/3/037502/pdf

Review of magnetic properties and magnetocaloric effect in the intermetallic compounds of rare earth with low boiling point metals

Magnetic properties were investigated on a single-crystalline DyB 2 C 2 compound with the tetragonal structure. Spontaneous magnetizations appear along the a- and [1 1 0]-directions below T C =15.3 K. A very small shoulder is observed only along the c -axis at T Q =24.7 K, although large λ-type anomalous specific heats are observed at T C and T Q . There exists a large magnetic anisotropy in the tetragonal basal plane which is observed in magnetization processes below T C . Neutron powder diffraction experiments reveal that magnetic reflections are observed only below T C . In the magnetically ordered phase, the Dy moments are arranged to be perpendicular to neighbors along the c -axis. The results are well interpreted by postulating that the phase between T C and T Q is an antiferroquadrupolar ordered one. DyB 2 C 2 is a novel compound with a high antiferroquadrupolar ordering temperature of 24.7 K.

Antiferroquadrupolar ordering and magnetic properties of the tetragonal DyB2C2 compound

Specific-heat, resistivity, neutron-spectroscopy, magnetization, and magnetostriction experiments on TmZn are reported. This equiatomic metallic compound crystallizes with the cubic CsCl structure and shows a first-order Jahn-Teller transition to a tetragonal structure at ${T}_{Q}=8.55$ K. The cell distortion reaches $\frac{c}{a}\ensuremath{-}1=(\ensuremath{-}9\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. The magnetic moment orders along a fourfold axis at ${T}_{c}=8.12$ K, its value being largely field dependent. Due to the vicinity of the transitions, they are mixed and strongly raised in temperature by (even low) applied fields as observed by the magnetization and magnetostriction experiments in the paramagnetic state. These results and the elastic constants previously published are analyzed taking into account the quadrupole-quadrupole exchange and the quadrupole-lattice term beside the Heisenberg exchange and the cubic crystal electric field (CEF) terms; the CEF parameters are ${A}_{4}〈{r}^{4}〉=\ensuremath{-}38\ifmmode\pm\else\textpm\fi{}5$ K and ${A}_{6}〈{r}_{6}〉=\ensuremath{-}19.6\ifmmode\pm\else\textpm\fi{}2$ K/atom. The ground state is the magnetic triplet ${\ensuremath{\Gamma}}_{5}^{(1)}$ in the cubic paramagnetic state. The theoretical study of the dependence of ${T}_{c}$ and ${T}_{Q}$ on the bilinear and biquadratic exchange terms reveals a complex phase diagram. In the case of TmZn, the obtained second-order coefficients allow a good description of all the physical properties now investigated.

Cooperative Jahn-Teller effect in TmZn

The magnetoelastic properties of the ferromagnetic cubic compounds of heavy rare earths with zinc ($R\mathrm{Zn}$) are investigated. Lattice distortions occuring below the ordering point are particularly strong when tetragonal: For instance, DyZn exhibits at low temperature a spontaneous tetragonal strain expressed as $\frac{c}{a}\ensuremath{-}1=+8.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. All of these magnetoelastic properties are chiefly due to the crystalline electric field splitting of the ground-state $J$ multiplet. But the tetragonal distortion observed in GdZn below the ordering point reveals pseudodipolar magnetoelastic effects to be important also; this contribution is taken into account for all the compounds. From our strain gauges and capacitance dilatometer experiments we deduce the one-ion and two-ion magnetoelastic coefficients across the series. The former ones are compared with determinations from ultrasonic measurements and their variation through the series is interpreted in terms of crystal-field theory. Finally, an attempt was made to connect these coefficients to the present knowledge of the conduction band in these CsCl-type intermetallic compounds.

Magnetoelastic properties of R Zn equiatomic compounds

A susceptibility formalism is developed for analyzing the magnetic and quadrupolar interactions in hexagonal and tetragonal rare-earth compounds. Symmetrized expressions are given for the one-ion magnetoelastic coupling and for the two-ion quadrupolar interactions. This formalism, derived from perturbation theory, leads to specific magnetic, strain, and quadrupolar susceptibilities considering both the crystalline-electric-field effects and quadrupolar interactions. It allows an analytical description of physical properties, such as the first- and third-order paramagnetic susceptibilities, the parastriction, and the elastic constants.

Susceptibility formalism for magnetic and quadrupolar interactions in hexagonal and tetragonal rare-earth compounds.

The rare-earth oxide compound ${\mathrm{HoVO}}_{4}$ (tetragonal zircon structure) is investigated in the extended susceptibility formalism, which includes all the features of the crystalline electric field in the analysis of the magnetic, magnetoelastic, and elastic properties as a function of temperature. The characteristic behavior of the first-order magnetic susceptibility allows us to refine the values of the crystalline electric-field parameters and to determine the strength of the magnetic interactions. The magnetoelastic coefficients are then found from third-order magnetic susceptibility, parastriction, and elastic-constants measurements for the different symmetry modes. Their coherency with values determined for ${\mathrm{TbPO}}_{4}$ is then emphasized: They have the same sign and order of magnitude; in particular the magnetoelastic coefficients for the tetragonal symmetry are sizable in these rare-earth oxides in contrast to the case of rare-earth intermetallics. The unusual temperature dependence of the third-order magnetic susceptibility along the tetragonal axis is a precursor of the level crossing in high magnetic fields associated with a magnetization jump of about 8${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ at 11.4 T, which we study as a function of temperature down to 0.1 K. The existence of a two-step jump of the magnetization at low temperatures, if not driven by mechanical stresses, remains an intriguing result.

J. Rouchy

Papers

Cooperative Jahn-Teller effect in TmZn

Magnetoelastic properties of R Zn equiatomic compounds

Susceptibility formalism for magnetic and quadrupolar interactions in hexagonal and tetragonal rare-earth compounds.

Magnetoelastic properties and level crossing in HoVO4.

Magnetic and quadrupolar properties of DyCu and related dysprosium cubic compounds